This paper presents a solution to the test time minimization problem for core-based systems that contain sequential cores with STUMPS architecture. We assume a hybrid BIST approach, where a test set is assembled, for each core, from pseudorandom test patterns that are generated online, and deterministic test patterns that are generated offline and stored in the system. We propose a methodology to find the optimal combination of pseudorandom and deterministic test sets of the whole system, consisting of multiple cores, under given memory constraints, so that the total test time is minimized. Our approach employs a fast estimation methodology in order to avoid exhaustive search and to speed-up the calculation process. Experimental results have shown the efficiency of the algorithm to find near optimal solutions.